let E be set ; :: thesis: for A being Subset of (E ^omega )
for k being Nat holds (A + ) ^^ (A |^.. k) = A |^.. (k + 1)
let A be Subset of (E ^omega ); :: thesis: for k being Nat holds (A + ) ^^ (A |^.. k) = A |^.. (k + 1)
let k be Nat; :: thesis: (A + ) ^^ (A |^.. k) = A |^.. (k + 1)
thus (A + ) ^^ (A |^.. k) = (A |^.. 1) ^^ (A |^.. k) by Th50
.= A |^.. (k + 1) by Th18 ; :: thesis: verum